In one such known mounting device (cf. catalogue "Zielfemrohrmontage" [Telescopic sight mount] of the company Ernst Apel, W-8708 Gerbrunn-Wurzburg, April 1988, page 58), the two fixed jaws have dovetail formed undercuts. The receiver itself is provided with a prism running in the barrel direction, whose dovetail form, undercut side surfaces form the clamping surfaces for the jaws. The telescopic sight is normally screwed fast to the mounting bridge, as usual. To mount the telescopic sight on the rifle the mounting bridge is brought into abutment with its two fixed jaws in abutment with one of the side faces of the prism and it is then tilted towards the rifle about an axis running parallel to the barrel axis, whereby the movable jaws move into the region of the other side surface of the prism. At the same time as the tilting movement, a fixing pin on the underside of the mounting bridge comes into engagement with a transverse groove provided in the prism. This fixing pin serves to transfer the forces in the barrel direction from the receiver to the mounting bridge and vice versa. After the mounting bridge has been tilted on the prism of the receiver (this known mounting device is accordingly known as a "tilt mount"), the nut is actuated and the movable, undercut jaw is thereby clamped against the other side of the prism. In this known mounting device, the movable jaw is in the middle between the two fixed jaws, whereby a 3-point support of the mounting bridge on the receiver is effected. However, the manufacture of the dovetail form undercut clamping surfaces on the prism of the receiver requires substantial expense, since these surfaces must be precisely parallel to one another and to the barrel axis. Moreover it is necessary in forming the prism to provide an upwardly extending extension on the receiver, since the receiver would otherwise be too greatly weakened by the dovetail form undercutting extending over the whole length thereof in the region of the cartridge chamber. Additional weight results from the upwardly projecting extension and the telescopic sight axis moreover assumes a greater distance from the barrel axis. The fixing pin, which has to be separately made and attached to the mounting bridge, as well as the transverse groove for its engagement in the prism require additional working steps in the manufacture. The 3-point support of the mounting bridge on the prism is not particularly stable, so that the known mounting device is only suitable for small, light telescopic sights. Moreover the 3-point support has the disadvantage that the mounting bridge can move during the tightening of the movable jaw, so that an aiming point offset can arise.